Autrici: Mariagrazia Visconti e Bruna Pisano - Politecnico di Torino,  2018


The present work is a numerical study of the aero-acoustic phenomena occurring in a sub-scaled cold flow model of large solid propellant boosters such as the Ariane 5 solid rocket motor (SRM). In fact, the aero-acoustic instabilities bring pressure and thrust oscillations that can reduce the performance of a propeller and that could damage the payload.


                                                                                             Figure 1: Aero-acoustic phenomenon inside the engine

The booster in figure 1 consists of a solid propellant, whose grain is segmented by two inhibitor rings that act as thermal protectors, moreover, a submerged nozzle is integrated into the last segment of the solid propellant. During combustion as shown in figure 2, the regression of the solid propellant, sur- rounding the nozzle integration, leads to the formation of a cavity whose volume varies during the launch.



                      (a) Beginning of the launch                                          (b) During the launch                                          (c) Ending of the propellant


                                                     Figure 2: Schematization of the combustion chamber at different times

The pressure oscillations develop in a confined flow, established in the engine and they are the result of a coupling between the hydrodynamic instabilities and the longitudinal acoustic modes of the combustion chamber. The hydrodynamic instabilities are characterized by the presence of obstacles OVS in figure 3a, or due to flow phenomena linked to the presence of sidewalls PVS, in figure 3b.


                                     (a) Obstacle Vortex Shedding                                                                                                           (b) Parietal Vortex Shedding


                                                                                            Figure 3: Hydrodynamic instabilities: OVS and PVS

These are the mechanisms that drive pressure fluctuations when the dispersion frequency adapts to one of the acoustic chamber resonance modes. The level of pressure fluctuations achieved under resonance conditions is controlled by an interaction between nozzle and vortex.



                                                                                       Figure 4: Aero-acoustic coupling phenomenon scheme

The former aim of this work, starting from the validation of the modeling with data found in literature [1], consists in looking for the effect of the nozzle cavity on the acoustic coupling of the flow and therefore on the consequent pressure oscillations in SRM.

To this end, three different geometries of the nozzle cavity have been configured and investigated. Looking at the figure 5, it is easy to distinguish the regions, in particular, it should be noted that the flow of cold air is injected axially into the inlet region.


                                                                                       (a) Nominal cavity configuration - Cavity A      


                                                                                         (b) Reduced cavity configuration - Cavity B    


                                                                                       (c) No cavity configuration - Cavity C

Figure 5: The axial injected flow configuration, geometry of the numerical domain, boundary conditions and position of the virtual sensors for each configuration.

The calculation grids have been built by refining the areas of greatest interest depending on the configuration taken into analysis. In particular, the area where the inhibitor is placed, the walls and the area relative to the nozzle and the cavity of the combustion chamber have been mostly refined.

The graphic representation of the adopted mesh with the first configuration - Cavity A - has been reported in figure 6, by way of example. It consists of 178637 elements, 639715 nodes and 855375 faces. All the results have been obtained using the CFD software Sc-Flow.



                                                             (a) Overview of the mesh                                                             (b) Details of: cavity, obstacle and nozzle


                                                            Figure 6: Representation of mesh into numerical domain

Numerical simulations, in compressible, unsteady and axisymmetric flow conditions, have been simulated using the Large Eddy Simulation, LES, turbulence modeling. Furthermore, in order to obtain the convergent unstable signal, the simulations have been performed for about one hundred thousand iterations. Once the convergent unstable solution is reached, the simulation has been restarted for a physical time of T = 0.2s.

Manipulating, through the Fast Fourier Transform, the pressure data obtained from these transient analyses, it has been possible the determination of the pressure spectra at several points within the chamber. In fact, in order to investigate the flow field features and the pressure oscillation phenomena, at significant points inside the combustion chamber, virtual sensors have been placed.

Thus, to be able to compare the obtained pressure spectra for each geometry, reference was made to a particular sensor that is placed in the origin of the reference system.  The resulting pressure spectrum at the virtual sensor 8 has been reported   in the figure 7 for each configuration.

Cavity A - Submerged nozzle
(a) Cavity A - Submerged nozzle
Cavity B - Reduced cavity
(b) Cavity B - Reduced cavity
Cavity C - No cavity
(c) Cavity C - No cavity

Figure 7: Pressure spectra at sensor 8 for each cavity configuration

Furthermore, it has been possible to define a sequence of vorticity. In figure 8, for each analyzed geometry, a single exemplary frame of the vorticity field within the combustion chamber has been shown.

(a) Cavity A

(b) Cavity B

(c) Cavity C

Figure 8: Vorticity fields

Each vortex developed behind the thermal protection impinges on the nozzle head and breaks. Part of it interacts with the vortices already present in the upper cavity, while the other one escapes through the nozzle.

The comparison with the obtained data has been carried out in order to validate    the adopted software and the configured modeling. The vorticity field has been accurately reproduced by the modeling. The OVS and PVS instabilities have been identified.   The geometry of the nozzle has been modified in order to detect the effect of the variation of the nozzle cavity volume on the pressure oscillations and, consequently, on the flow-acoustic coupling.

The main outcome from the presented work is evidently that the flow-acoustic coupling is a phenomenon that strongly occurs in presence of nozzle cavity. In fact, the geometry of the nozzle has got a significant effect on Pressure Oscillations through a coupling between the acoustic fluctuations induced by the cavity volume and the vortices shedding in front of the entrance to the cavity. Indeed, the pressure oscillations are influenced by the interaction of the vortex with the nozzle head.  It   has been observed that as the volume of the nozzle cavity decreases, the pressure fluctuations are damped. Hence, the trend of the maximum sound pressure level, obtained from the Pressure Spectra of the three configurations analyzed, has been traced. The trend of the pressure amplitudes results almost linear with the volume of the cavity.


                                                                                         Figure 9: Nozzle cavity effect trend

Subsequently a more truthful situation is reproduced in which the flow is injected radially to simulate the entrance of the combustion gases coming from the side walls.


                                                                                        Figure 10: Regions of interest - Radial injected flow configuration with inhibitor

Also, these cases have been carried out with the same flow conditions. Furthermore, in order to obtain the convergent unstable signal, the simulations have been performed for about two hundred thousand iterations. Once the convergent unstable solution is reached, the simulation has been restarted for a physical time of T = 0.2s.


                                                                                                                                                                                                     a. Configuration with the inhibitor                                                          b. Configuration without the inhibitor


                        Figure 11: Vorticity fields

Various configurations have been tested in order to identify the actual role of each parameter in play on pressure oscillations. In fact, as shown in figure 12, in the absence of the inhibitor, the pressure spectra has been shown much lower values than the cases in which this element is present. In figure 13, the configuration with radially injected flow, rather than axially, has been shown an increase in the Vortex Shedding period with a consequent decrease in the frequencies and a reduction of the pressure oscillation values.


                                                               Figure 12: Comparison between radial injected cases: configuration with and without the inhibitor, point 8   



                                                            Figure 13: Comparison between case with radial and axial injected flow, point 8



[1]J. Anthoine (2000), Experimental and numerical study of aeroacustic phenomena in large solid propellant boosters, Université libre de Bruxelles, Bruxelles.